Inversion formula and Parseval theorem for complex continuous wavelet transforms studied by entangled state representation

doi:10.1088/1674-1056/19/7/074205

中国物理B ›› 2010, Vol. 19 ›› Issue (7): 74205-074205.doi: 10.1088/1674-1056/19/7/074205

Inversion formula and Parseval theorem for complex continuous wavelet transforms studied by entangled state representation

胡利云¹, 范洪义²

(1)College of Physics and Communication Electronics, Jiangxi Normal University, Nanchang 330022, China; (2)Department of Physics, Shanghai Jiao Tong University, Shanghai 200030, China

收稿日期:2009-10-28 修回日期:2010-02-01 出版日期:2010-07-15 发布日期:2010-07-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 10775097), and the Research Foundation of the Education Department of Jiangxi Province of China (Grant No. GJJ10097).

Inversion formula and Parseval theorem for complex continuous wavelet transforms studied by entangled state representation

Hu Li-Yun(胡利云)^a)†ger and Fan Hong-Yi(范洪义)^b)

^a College of Physics and Communication Electronics, Jiangxi Normal University, Nanchang 330022, China; ^b Department of Physics, Shanghai Jiao Tong University, Shanghai 200030, China

Received:2009-10-28 Revised:2010-02-01 Online:2010-07-15 Published:2010-07-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 10775097), and the Research Foundation of the Education Department of Jiangxi Province of China (Grant No. GJJ10097).

摘要/Abstract

摘要： In a preceding letter (2007 Opt. Lett. 32 554) we propose complex continuous wavelet transforms and found Laguerre—Gaussian mother wavelets family. In this work we present the inversion formula and Parseval theorem for complex continuous wavelet transform by virtue of the entangled state representation, which makes the complex continuous wavelet transform theory complete. A new orthogonal property of mother wavelet in parameter space is revealed.

Abstract: In a preceding letter (2007 Opt. Lett. 32 554) we propose complex continuous wavelet transforms and found Laguerre—Gaussian mother wavelets family. In this work we present the inversion formula and Parseval theorem for complex continuous wavelet transform by virtue of the entangled state representation, which makes the complex continuous wavelet transform theory complete. A new orthogonal property of mother wavelet in parameter space is revealed.

Key words: Parseval theorem, complex continuous wavelet transforms, entangled state representation

中图分类号: (Entanglement and quantum nonlocality)

03.65.Ud

42.50.Dv (Quantum state engineering and measurements) 42.30.Kq (Fourier optics)

胡利云, 范洪义. Inversion formula and Parseval theorem for complex continuous wavelet transforms studied by entangled state representation[J]. 中国物理B, 2010, 19(7): 74205-074205.

Hu Li-Yun(胡利云) and Fan Hong-Yi(范洪义). Inversion formula and Parseval theorem for complex continuous wavelet transforms studied by entangled state representation[J]. Chin. Phys. B, 2010, 19(7): 74205-074205.

参考文献 16

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[4]	Goodman J W 1968 Introduction to Fourier Optics (New York: McGraw-Hill)
[5]	Hu L Y and Fan H Y 2008 J. Mod. Opt. 55 1835
[6]	Fan H Y and Lu H L 2006 Opt. Lett. 31 407
[7]	Fan H Y and Lu J F 2004 Commun. Theor. Phys. 41 681
[8]	Fan H Y and Klauder J R 1994 Phys. Rev. A 49 704
[9]	Fan H Y and Lu H L 2007 Opt. Lett. 32 554
[10]	Wunsche A 2000 J. Phys. A Math. and Gen. 33 1603
[11]	Loudon R, and Knight P L 1987 J. Mod. Opt. 34 709
[12]	Scully M O and Zubairy M S 1997 Quantum Optics (Berlin: Cambridge University)
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[15]	Fan H Y and Hu L Y 2009 Chin. Phys. B 18 0611
[16]	Fan H Y and Hu L Y 2008 Chin. Phys. B 17 1640 endfootnotesize

Inversion formula and Parseval theorem for complex continuous wavelet transforms studied by entangled state representation

Inversion formula and Parseval theorem for complex continuous wavelet transforms studied by entangled state representation

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